Electro-optic modulation

ABSTRACT

A silicon electro-optic waveguide modulator is formed using a metal-oxide-semiconductor (MOS) configuration. Various embodiments are described using different modes of operation of the MOS diode and gate oxide thicknesses. In one example, a high-speed submicron waveguide active device is formed using silicon-on-insulator. A micro-ring resonator intensity-modulator exhibits switching times on the order of tens of pS with modulation depth of 73% with a bias voltage of 5 volts.

RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 11/367,756, filed Mar. 3, 2006, which applicationclaims priority to U.S. Provisional Application Ser. No. 60/658,536(entitled Electro-Optic Modulation, filed Mar. 4, 2005) which isincorporated herein by reference.

GOVERNMENT FUNDING

The invention described herein was made with U.S. Government supportunder Contract No. ECS-0300387 awarded by National Science Foundation(NSF), under contract 2003-IT-674 awarded by DARPA, and under Grant No.ECS-9731293 awarded by the National Science Foundation. Further supportwas provided under grant No. F49620-03-1-0424 from AFOSR (Dr. GernotPomrenke). The United States Government has certain rights in theinvention.

BACKGROUND

Metal interconnections are expected to become a bottleneck ofperformance of electronic systems as transistors continue to scale tosmaller sizes. Optical interconnections, implemented at different levelsranging from rack-to-rack down to chip-to-chip and intra-chipinterconnections could enable low power dissipation, low latencies andhigh bandwidths. The realization of such small scale opticalinterconnections relies on the ability to integrate micro-opticaldevices with the microelectronics chip. The recent demonstrations ofsilicon low-loss waveguides, amplifiers and lasers advance thisintegrative goal, but a silicon electro-optic modulator with a sizesmall enough for chip-scale integration is needed.

SUMMARY

A high-speed electro-optical modulator is formed in highly compactstructures. The modulator is based on a light-confining structure thatenhances the sensitivity of light to small changes in refractive indexand also enables high speed operation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a layout schematic of a ring resonator based modulator with aninset showing a schematic of the cross-section of the ring according toan example embodiment.

FIGS. 2A and 2B are a top-view SEM picture of the ring coupled to thewaveguide with a zoom-in picture of the coupling region, and a top-viewmicroscopic picture of the ring resonator after the metal contacts areformed according to an example embodiment.

FIG. 3 is a graph of a transmission spectrum of the ring resonator atthe bias voltage of 0.58 V, 0.87 V, and 0.94 V, respectively with aninset showing a transfer function of the modulator for light withwavelength of 1573.9 nm according to an example embodiment.

FIGS. 4A and 4B are waveforms of a driving voltage an output opticalpower when a ring resonator based modulator is driven by 32-bit randomdata sequences at the data rate of 400 Mbps according to an exampleembodiment.

FIGS. 5A, 5B and 5C are schematic cross-sections of MOShigh-index-contrast SOI rib waveguides for 1.55-μm wavelength with threedoping schemes are shown: A) for inversion, B) for accumulation and C)for depletion operation according to example embodiments.

FIGS. 6A and 6B are graphs for first and second embodiments illustratingsteady-state effective refractive index variation as a function of theabsolute voltage of the gate voltage for inversion (squares),accumulation (circles) and depletion (triangles) operation modes forgate oxide thicknesses of a) h_(gox)=100 nm and b) h_(gox)=200 nm, wherethe applied voltage is negative for the inversion and accumulation modesand positive for the depletion mode.

FIG. 7 illustrates steady-state carrier 2-D distribution in an Si corewaveguide for the depletion-mode operation with a gate voltage isV_(g)=20 V and h_(gox)=200 nm.

FIG. 8 illustrates optical losses for a first embodiment of the TE-likefundamental mode as a function of the absolute value of the gate voltagefor inversion (squares), accumulation (circles) and depletion(triangles) operation modes for gate oxide thicknesses of h_(gox)=100 nmand h_(gox)=200 nm.

FIG. 9 illustrates optical losses for a second embodiment as a functionof the absolute value of the gate voltage for inversion (squares),accumulation (circles) and depletion (triangles) operation modes forgate oxide thicknesses of h_(gox)=100 nm and h_(gox)=200 nm.

FIGS. 10A and 10B illustrate fundamental optical mode profile for a)h_(gox)=100 nm and b) h_(gox)=200 nm for a first embodiment.

FIGS. 11A and 11B illustrate TE-like fundamental optical mode profilesfor a) h_(gox)=100 nm and b) h_(gox)=200 nm for a second embodiment.

FIGS. 12A, 12B and 12C illustrate A) Effective refractive indexvariation of the TE-like fundamental mode as a function of the absolutevalue of the ON-state gate voltage for depletion-mode under pulse(triangles) and de (circles) operation and for the accumulation-mode(squares), B) Optical losses for the same configurations, and C) opticallosses for a second embodiment, where dashed lines indicate that the Sibreakdown electric field has been exceeded, the gate oxide thickness ish_(gox)=200 nm, and the applied voltage is negative for the accumulationcase and positive for the depletion mode.

FIG. 13 illustrates a high-index-contrast waveguide electro-opticmodulator based on a microring resonator and a MOS diode where thecomplex refractive index of the resonant region is changed by applying abias voltage to the gate electrode.

FIG. 14 illustrates spectral transmittance (out port) for the TE-likefundamental optical mode of the simulated electro-optic MOS Si microringmodulator (accumulation configuration) for V_(g)=0V (OFF state) andV_(g)=−5V (Δn=−6.3×10⁻⁵, ON state) for a ring radius of R=6.9 μm, wherecircles illustrate the modulation depth at λ_(p)=1550.014 nm.

FIG. 15 illustrates calculated modulation depth of the electro-optic MOSmicroring resonator for the accumulation (squares) and depletion(circles) modes where the probe wavelengths are 1550.014 nm and 1549.975nm for the accumulation and depletion cases, respectively and thetransmittivity in the OFF state at the corresponding probe wavelengthwas calculated to be 59% and 23% for the accumulation and depletioncases, respectively.

FIG. 16 illustrates a high-index-contrast waveguide electro-opticmodulator based on a microcavity and a MOS diode, where the complexrefractive index of the resonant region is changed by applying a biasvoltage to the gate electrode.

FIG. 17 illustrates calculated modulation depth of the electro-optic MOSmicrocavity for the accumulation (squares) and depletion (circles)modes, where dashed line indicates that the Si breakdown electric fieldhas been exceeded, the probe wavelengths are 1550.04 nm and 1549.91 nmfor the accumulation and depletion cases, respectively and thetransmittivity in the OFF state at the corresponding probe wavelengthwas calculated to be 50% and 33% for the accumulation and depletioncases, respectively.

FIG. 18 illustrates spectral transmittance for the TE-like fundamentaloptical mode of the simulated electro-optic MOS Si modulator forV_(g)=0V (OFF state) and V_(g)=−5V (Δn=−6×10⁻⁵, ON state) for a21.56-μm-long cavity, where circles illustrate the modulation depth atλ_(p)=1.55004 μm.

FIG. 19 is a schematic diagram of a ring resonator based opticalmodulator using the pin effect.

FIG. 20 is a schematic diagram of a ring resonator based opticalmodulator using the MOS effect.

DETAILED DESCRIPTION

In the following description, reference is made to the accompanyingdrawings that form a part hereof, and in which is shown by way ofillustration specific embodiments which may be practiced. Theseembodiments are described in sufficient detail to enable those skilledin the art to practice the invention, and it is to be understood thatother embodiments may be utilized and that structural, logical andelectrical changes may be made without departing from the scope of thepresent invention. The following description is, therefore, not to betaken in a limited sense, and the scope of the present invention isdefined by the appended claims.

Sections of the following text describe different example embodiments ofthe invention. A first section describes an ultra-compact siliconelectro-optic modulator. A second section describes high speedelectro-optic modulation in high confinement silicon waveguides usingmetal-oxide-semiconductor (MOS) configurations. A third section providesa description of MOS geometries for integrating MOS and p-i-nstructures.

Ultra-Compact Silicon Electro-Optic Modulator

Electro-optical control of light on silicon is challenging due to itsweak electro-optical properties. The large dimensions of previouslydemonstrated structures were necessary in order to achieve a significantmodulation of the transmission in spite of the small change ofrefractive index of silicon.

Light confining resonating structures can enhance the effect ofrefractive index change on the transmission response. Ring resonatorshave been used for all-optical modulation. The optical properties of onedevice was changed by using one beam of light to optically injectingfree carriers and therefore control the flow of another beam of light. Adoped ring resonator may have intrinsic carriers, which can be modulatedby application of reverse bias voltages, affecting the flow of light.

A schematic of an example electro-optic modulator is shown in FIG. 1generally at 100. The modulator 100 consists of a ring resonator 105coupled to a single waveguide 110. The transmission of a ring resonator,coupled to a waveguide, is highly sensitive to the signal wavelength andis greatly reduced at wavelengths in which the ring circumferencecorresponds to an integer number of guided wavelengths. By tuning theeffective index of the ring waveguide 105, the resonance wavelength ismodified which induces a strong modulation of the transmitted signal.

The effective index of the ring is modulated electrically by carrierinjection using a p-i-n junction 115 in the inset, embedded in thewaveguide forming the ring resonator. The inset of FIG. 1 shows thecross-section of this waveguide. It consists of a strip waveguide 120formed on a thin 50-nm thin slab layer 125. Since the thickness of theslab is much smaller than the wavelength propagating in the device (1.5μm), the mode profile of this waveguide is very close to that of a SOIstrip waveguide. Highly doped p and n regions are defined around thering using ion implantation as indicated at 130 and 135 respectively.Ohmic contacts are deposited on the doped regions at 140 and 145. Inorder to minimize absorption losses, the doped regions are formedapproximately 1 μm away from the ring resonator, ensuring that theoverlap of the resonating mode with the doped regions is minimal. Avoltage source 150 is coupled to the ohmic contacts to tune theeffective index of the ring waveguide 105 and thus modulate lighttransmission. A scanning electron microsope image of an examplemodulator is shown in FIGS. 2A and 2B, wherein the numbering is similarto that in FIG. 1.

In one embodiment, the p-i-n ring resonator is formed on a SOI substratewith 3-μm buried oxide layer. Both the waveguide coupling to the ringand the one forming the ring have width of 450 nm and height of 250 nm.The diameter of the ring is approximately 12 μm, and the spacing betweenthe ring and the straight waveguide is 275 nm. In order to ensure highcoupling efficiency between the waveguide and the incoming opticalfiber, nanotapers may be fabricated at the ends of the waveguide. Ananotaper is basically a narrowing of the waveguide to one or morenanometer size ends, which may be optically efficiently coupled to anoptical fiber or larger waveguide structure. The structures may bedefined using lithography followed by reactive ion plasma etching (RIE).After etching of the ring resonator structure, doping regions may bedefined using photolithography, and doping may be accomplished by ionimplantation. After ion implantation, a 1-μm thick silicon oxide layermay be deposited onto the wafer using plasma enhanced chemical vapordeposition. Vias are then opened into the oxide using photolithographyand plasma etching for depositing the metal contacts. Dimensionsreferred to in these embodiments may be varied significantly, such as toobtain structures that resonate at different frequencies. Process stepsmay also be performed in different ways, and are described simply toillustrate one example method of fabricating the structures. In variousembodiments, the radius of the ring may vary between approximately 1 anda few hundred microns.

FIG. 3 shows the relative transmission through the modulator around theresonance of 1574 nm at different bias of the p-i-n junction. The solidcurve 310 shows the spectrum when the p-i-n junction is biased belowthreshold of the diode, and the current through the junction is belowone detection limit (0.1 μA). The spectrum shows a 15-dB drop oftransmission at the resonant wavelength of 1574.9 nm. The 3-dB bandwidthof the resonance Δλ is 0.04 nm measured from the spectrum, correspondingto a quality-factor, defined as Q=λ/Δλ, of 39350. This Q factorcorrespond to cavity photon lifetimes of τ_(cav1)=λ²/(2πcΔλ_(FWHM1))=33ps, where c is the speed of light in vacuum. Thus, despite the resonantnature of the structure, the photon confinement of modulator does notlimit its speed. The small ripples (˜1 dB) on the waveform originatefrom the reflections at both ends of the waveguide, which can beeliminated by anti-reflection coating. The carrier density in the cavityincreases as the forward bias on the p-i-n junction increases. Thedashed and dotted curves 320, and 330 in FIG. 3 show the spectra whenthe bias voltage is 0.87 V and 0.94 V, and the current is 11.1 μA and19.9 μA, respectively. In both cases the resonance is blue shifted dueto the lowering of effective index caused by the increase of carrierdensity. The depths of the notches in the spectra also decrease, due tothe increased absorption loss in the ring induced by the injectedcarriers. Comparing the curves in FIG. 3, one can see that at thewavelength of 1573.9 nm, 97% modulation can be obtained with less than0.3 V bias voltage change. At this wavelength, since light does notcouple to the ring when the free carriers are generated, the absorptionof free carriers does not cause any extra loss to the light.

The light confining nature of the modulator not only enables shrinkingof the device size, but also enables high speed operation under p-i-nconfiguration. The p-i-n configuration of the modulator, as opposed tothe MOS configuration, is important for achieving high modulation depth,since the overlap between the region where the index is changed and thewaveguide mode index changes is large. However, p-i-n devices have beentraditionally considered as relatively slow devices when compared to MOSones. In these devices, while extraction of carriers in reverse biasedoperation can be fast, down to tens of ps, carriers injection in forwardbias operation is slow, limited by the rise time of the p-i-n, on theorder of 10 ns. The resonating nature of the modulator removes thisspeed limitation. The inset 340 of FIG. 3 shows the transfer function ofthe device, i.e., the transmission of the modulator at the wavelength of1573.9 nm with different bias voltages. This transfer function showsthat the resonating nature of the device enables voltages larger that0.9V to be applied without modifying the transmission response (T˜1).This is because at these voltages the resonance of the device iscompletely detuned from the probe wavelength. This insensitivity of theoptical transmission at higher bias voltage is in strong contrast toMach Zender modulators, in which higher voltage affect strongly thetransmission. When the device is operation at higher voltages, theoptical transmission goes to ˜1 well before the PIN junction reaches itssteady state. This means that the optical rise time can be far less thanthe electrical rise time of ˜10 ns at high forward biasing, which iscrucial for achieving high speed modulation.

In order to measure the dynamic response of the modulator, a 0.4 Gbit/selectrical signal generated by a pulsed pattern generator is used todrive the modulator. The peak-to-peak voltage (Vpp) of the signal is 3.3V. The output the waveguide is sent to a 12-GHz detector and thewaveform is recorded on an oscilloscope. FIGS. 4A and 4B show both thedriving data pattern 410 and the optical output 420, demonstrating highmodulation depths depths at 0.4 Gb/sec. On FIG. 4B an approximately 1.2ns optical rise time is shown. Reducing the contact resistance,currently measured to be about 4 kΩ in one example device, to a typicalvalue of 100 ohm would reduce the rise time to less than 0.1 nsec forthe same applied voltage, enabling its operation at speeds higher than 5Gbps at 3 Vpp.

The wavelength selective modulation property of the modulator can beutilized for building wavelength division multiplexing (WDM)interconnections, which can greatly extend the bandwidth of opticalinterconnections. Given the short length of the modulator (<20 μm) andthe waveguide propagation loss of approximately 4+/−1 dB/cm, theinsertion loss of the modulator itself is negligibly to light withwavelength detuned from the ring resonance. The small insertion loss ofthe modulator makes it possible to cascade multiple modulators along asingle waveguide and modulate independently each WDM channel.

High-Speed Electro-Optic Modulation in High Confinement SiliconWaveguides Using Metal-Oxide-Semiconductor Configurations.

The electrical and optical properties of a silicon electro-opticwaveguide modulator using a metal-oxide-semiconductor (MOS)configuration are described. Device performance may be observed underdifferent modes of operation of a MOS diode and gate oxide thicknessesas illustrated in FIGS. 5A, 5B and 5C. Calculations indicate that theseembodiments may be used for achieving high-speed submicron waveguideactive devices on silicon-on-insulator. A microring resonatorintensity-modulator is predicted to exhibit switching times on the orderof tens of ps with modulation depth of 73% by employing a bias voltageof only 5 V. In a further embodiment, a submicron-size one-dimensionalmicrocavity intensity-modulator is predicted to exhibit switching timeson the order of tens of ps with modulation depth of 19% by employing abias voltage of only 5 V.

The main methods to alter the refractive index in Si are thethermo-optic effect and the plasma dispersion effect. The thermo-opticeffect is rather slow and can be used only up to 1 MHz modulationfrequency. For higher speed, electro-optic devices are required.Unstrained pure crystalline Si does not exhibit linear electro-optic(Pockels) effect and the refractive index changes due to theFranz-Keldysh effect and Kerr effect are very weak. Therefore, the freecarrier dispersion effect is used to change electrically both the realrefractive index and optical absorption coefficient. In a furtherembodiment, the resonator structure may be doped, creating intrinsiccarriers. These carriers may also be modulated with a reverse biasvoltage to modulate the light.

The free-carrier concentration in Si electro-optic devices can be variedby injection, accumulation, depletion or inversion of carriers. P-i-ndiodes and metal-oxide-semiconductor field-effect-transistors (MOSFET)may be employed for this purpose. In a previous work, we proposed andanalyzed a waveguide active structure based on a p-i-n diode. Thatconfiguration was predicted to provide high modulation depth for verylow power consumption. The switching time was calculated to be around1.29 ns, limited by carrier diffusion (carrier injection process). Theuse of a MOS diode should lead to higher speed operation since thecarrier distribution in the semiconductor is governed by a driftmechanism (electric field). Additional advantages of a MOS configurationare negligible dc power consumption and the fact that the refractiveindex change is localized under the gate electrode, and therefore nocarrier confinement methods (like isolation trenches in a p-i-n diode)are necessary. In a MOS structure however, in carrier depletion,accumulation or inversion configuration, significant large concentrationvariations are possible only within small distances (a few tens ofnanometers) beneath the insulated gate region. This produces a smalloverlap between the optical mode and the non-equilibrium chargedistribution in the waveguide, leading to a smaller effective indexvariation in a MOS system than that in a p-i-n configuration. A smallindex change requires a very long structure, on the order of millimeter,in order to induce a significant modulation depth.

In one embodiment of the present invention, a micron-size MOS-basedhigh-index-contrast SOI waveguide provides high-speed electro-opticmodulation in Si based on strong light confinement. The lightconfinement enhances the effect of small index changes on thetransmission of the device, enabling an ultra-compact structure withhigh modulation depth. In one embodiment, a studied high-index-contrastwaveguide structure permits, contrary to previous works, negligiblelosses for a radius of curvature as small as 5 μm, allowing theimplementation of high dense photonic circuits. In a further embodiment,a structure studied is based on sub-micron size high index contrastwaveguides, enabling contrary to previous works, negligible losses for aradius of curvature as small as 5 μm, allowing the implementation ofhigh dense photonic circuits.

FIGS. 5A, 5B and 5C show schematic cross-sections of variousMOS-waveguide configurations. The structures consist of a high aspectratio [rib height (200 nm)>>slab height (50 nm)] rib SOI waveguide 510,511 and 512, with highly doped regions (10¹⁹ cm⁻³) defined in the slab515, 516, and 517 at each side of the rib. The structures illustrated inFIGS. 5A, 5B and 5C operate under different mechanisms for modulation:carrier inversion (hole inversion layer) in FIG. 5A, hole accumulationin FIG. 5B and hole depletion operation regimes in FIG. 5C,respectively. The inversion and accumulation configurations are based onincreasing the hole concentration under the gate 520, 521 oxide 530, 531whereas the depletion configuration is based on decreasing the holeconcentration in the waveguide 512 core.

The silicon layer (device layer) has a background doping concentrationof 10¹⁵ cm⁻³ in FIG. 5A (n-type) and 5B (p-type), whereas a uniformdoping concentration of p=2×10¹⁷ cm⁻³ is considered in FIG. 5C. A ribcross section height and width dimension are considered to be the onestypical of a 1.55-μm-wavelength high-index-contrast strip SOI waveguide,that is, 250 nm and 450 nm, respectively, in order to guarantee singlemode operation. The distance of the doped regions to the rib sidewallsis 200 nm. In one embodiment, a 100-nm-thick and 450-nm-wide n-typehighly-doped (8×10¹⁸ cm⁻³) poly-Si layer acts as a gate electrode 520,521 and 522, whereas the lateral highly doped regions 540, 541, 541operate as ground (Gnd) electrodes. A top SiO₂ cladding layer 550, 551,552 covers the whole structure. In a further embodiment, a 100-nm-thickand 450-nm-wide metal (Au) layer acts as a gate electrode 520, 521 and522, whereas the lateral highly doped regions 540, 541 and 542 operateas ground (Gnd) electrodes.

From the values of the electron and hole concentrations at any point ofthe Si core waveguide (calculated with the electrical model describedbelow), the induced real refractive index and optical absorptioncoefficient variations (Δn and Δα, respectively) produced byfree-carrier dispersion at a wavelength of 1.55 μm are calculated byusing:

Δn=Δn _(e) +Δn _(h)=−[8.8×10⁻²² ·ΔN+8.5×10⁻¹⁸·(ΔP)^(0.8)]  [1]

Δα=Δα_(e)+Δα_(h)=8.5×10⁻¹⁸ ·ΔN+6.0×10⁻¹⁸ ·ΔP  [2]

where

Δn_(e) is the refractive index change due to electron concentrationchange;

Δn_(h) is the refractive index change due to hole concentration change;

ΔN is the electron concentration change in cm⁻³;

ΔP is the hole concentration change in cm⁻³;

Δα_(e) (in cm⁻¹) is the absorption coefficient variations due to ΔN;

Δα_(h) (in cm⁻¹) is the absorption coefficient variation due to ΔP.

Eq. 1 indicates that the effect on the refractive index of holes isapproximately three times larger than that due to electrons for the samecarrier concentration. Eq. 2 reveals that the contribution to theabsorption coefficient due to holes is lower than that due to electrons.These two facts justify the use of the hole distribution to vary therefractive index for all the MOS modes of operation illustrated in FIGS.5A, 5B and 5C.

A two-dimensional simulation package, ATLAS from SILVACO, may beemployed to achieve the electrical calculations. The device modelingsoftware may be used to analyze electro-optic modulators in SOIwaveguides. This program simulates internal physics and devicecharacteristics of semiconductor devices by solving Poisson's equationand the charge continuity equations for electrons and holes numerically.The surfaces of the waveguide have been considered oxide-passivated. Themain parameters used in the simulations are shown in Table I.

TABLE I Si refractive index, n_(Si), (λ = 1.55 μm)   3.43 SiO₂refractive index, n_(SiO), (λ = 1.55 μm)   1.46 Electron carrierlifetime, τ_(n), (ns)  700^(a) Hole carrier lifetime, τ_(p), (ns) 300^(a) Electron mobility, μ_(n), (cm²/Vs) 1000 Hole mobility, μ_(h),(cm²/Vs)  500 Electron Auger coefficient 8.3 × 10⁻³² Hole Augercoefficient 1.8 × 10⁻³¹ Si background carrier conc. (cm⁻³)   1 × 10¹⁵ Aurefractive index, n_(Au), (λ = 1.55 μm)   0.18^(b) Au absorptionconstant, k_(Au), (λ = 1.55 μm)  10.21^(b)

The following sections discuss the modal and geometry characteristics ofthe waveguide structure, and the variation of the effective refractiveindex and optical losses of the configurations illustrated in FIGS. 5A,5B and 5C for two gate oxide thicknesses, h_(gox)=100 nm and h_(gox)=200nm, as a function of the applied bias under steady-state conditions. Thedynamic characteristics of the MOS-waveguide under different operationregimes are also discussed.

In one embodiment, all the structures in FIGS. 5A, 5B and 5C exhibitsingle mode operation for both TE-like and TM-like polarization modesand gate oxide thicknesses h_(gox)=100 nm and h_(gox)=200 nm. Theconsidered distance of the highly-doped regions to the rib sidewalls(200 nm) and the slab thickness (50 nm) avoid excessive optical lossesfrom the highly-doped regions and enables implementing low-loss bentwaveguides with a radius of curvature as small as 5 μm.

Optical coupling from (to) an optical fiber to (from) the consideredhigh-index-contrast rib waveguide can be efficiently achieved by usingan inverse nanotaper. Mode delocalization can be used in order toeffectively bridge between the mode and index mismatch of indexsub-micron size waveguides and large fibers using compact structures.

Static characteristics are now discussed. In various embodiments, ahighly doped or metal gate electrode region may add significant opticallosses if its distance to the Si waveguide (h_(gox)) is too short, sinceit would overlap significantly with the optical mode field. On the otherhand, h_(gox) cannot be very long in order to allow for small operationvoltages. Therefore, a tradeoff must be found for the value of h_(gox).FIGS. 6A and 6B show the calculated effective refractive index change(Δn_(eff)) as a function of the absolute value of the gate voltage(V_(g)) for h_(gox)=100 nm and h_(gox)=200 nm, respectively, for thethree MOS operation modes. As expected, higher values of |Δn_(eff)| areobtained for h_(gox)=100 nm under the same operation mode.

The bias-dependencies of the accumulation- and inversion-modeconfigurations are similar for both values of h_(gox). In both cases, athin layer of holes is formed beneath the gate oxide. The holeconcentration in this layer increases with the absolute value of thegate voltage (negative). The values of |Δn_(eff)| are slightly higherfor the accumulation mode than for the inversion mode for the sameV_(g), because holes are majority carriers for the former regime andminority carriers in the latter, and therefore, higher holeconcentration values are obtained in the former. In both FIGS. 6A and6B, it is seen for the depletion case that, as the gate voltageincreases, Δn_(eff) initially increases due to the increase of thedepleted layer region; then Δn_(eff) reaches a maximum at a certainvoltage and it decreases as the gate voltage increases. This is becauseof the formation of an electron inversion layer beneath the gate oxidewhen the threshold voltage (V_(t)) of the MOS diode is exceeded (stronginversion condition). For the configuration of FIG. 5C, V_(t)=7.9 V and14.9 V for h_(gox)=100 nm and h_(gox)=200 nm, respectively. The increaseof carriers (electrons) produces an opposite effect (decrease ofn_(eff)) as that induced by the depleted region (increase of n_(eff)),reducing the total effective index variation. The inversion layerformation is illustrated in FIG. 7, which shows the hole and electrontwo-dimensional distribution in the Si core waveguide for the device ofFIG. 5C, V_(g)=20 V and h_(gox)=200 nm.

FIG. 8 illustrates calculated optical losses for the TE-like mode due tocarrier absorption in the semiconductor and the gate as a function ofthe gate voltage for the first embodiment. FIG. 9 illustrates thecalculated losses due to carrier adsorption in the semiconductor andmetal as a function of the gate voltage for the second embodiment,having metal contacts. The losses in both embodiments for h_(gox)=100 nmare considerably higher than those for h_(gox)=200 nm. This is becausethe optical mode overlaps significantly with the gate electrode forh_(gox)=100 nm, as shown in FIG. 10A for the first embodiment and FIG.11A for the second. Smaller overlap occurs for h_(gox)=200 nm (FIG. 10B,FIG. 11B). It is also observed in FIG. 8 that, for both values ofh_(gox), the losses for the depletion mode configuration are higher thanthose exhibited by the other two configurations, due to the backgrounddoping concentration of the Si waveguide (2×10¹⁷ cm⁻³). One can also seethat, as V_(g) increases, the depletion-mode losses initially decrease(increase of the depletion layer width), reach a minimum (atapproximately V_(t)) and then increase again (strong inversioncondition). Note however, that, as will be seen below, the losses forthe depletion case can be different under dynamic operation.

According to these results, under dc operation, the accumulation- or theinversion-mode configurations should be desirable since they exhibitlosses as low as 3.6 dB/cm for V_(g)=0 V (h_(gox)=200 nm) for the firstembodiment, and 15 dB/cm for 5V in the second embodiment. Thesimulations discussed so far are for TE-like polarization. For theTM-like mode the lower losses achievable are significantly higher, onthe order of 20 dB/cm (h_(gox)=200 nm) for the first embodiment and onthe order of 59 dB/cm for the second embodiment; therefore hereafter weconsider only the TE-like fundamental modes for the operation of thedevice. For the second embodiment, for TE-like mode, it is also deducedfrom the simulations that the thickness of the gate oxide should beh_(gox)=200 nm rather than h_(gox)=100 nm in order to avoid excessivelosses due to the metal gate electrode. A gate oxide thickness of 200 nmwill be also assumed for both embodiments in order to avoid excessivelosses due to the gate electrode.

The small-signal transient response determines the feasibility of thedevice to be used for high-speed data modulation. In the studiedconfigurations, the small-signal response will be defined by the MOStotal capacitance (C_(T)), which is given by the series combination ofthe gate oxide capacitance (C_(gox)) and the semiconductordepletion-region capacitance (C_(d)). The value of C_(gox) is constantand corresponds to the maximum capacitance of the system. The value ofC_(T) will depend on the operation mode of the MOS diode. Below, thesmall signal characteristics for the three modes of operation arediscussed for the various embodiments.

In the accumulation regime (FIG. 5B), there is no depletion region,therefore C_(T)=C_(gox). This capacitance remains the same under highfrequency operation. For h_(gox)=200 nm, we calculated a value ofC_(gox)=10⁻¹⁶ F/μm. Thus, assuming a load impedance of R=50Ω andC_(T)=C_(gox), the time constant τ_(c)=RC_(T) of the device results tobe 5×10⁻¹⁵ s/μm. For example, for a 20-μm-long device, τ_(c)=1×10⁻¹ ps,indicating the suitability of this configuration for high-speedoperation. The optical losses will be the same as those calculated inthe dc analysis for any operation frequency and gate voltage under theaccumulation mode of operation.

For the depletion-mode structure shown in FIG. 5C, the total capacitanceof the system will depend on the operation frequency and bias voltage.At low frequencies and V_(g)<V_(t), the total capacitance will besmaller than C_(gox) due to the depletion region capacitance. At lowfrequencies and V_(g)>V_(t) (strong inversion), the formation of theinversion layer makes the total capacitance equal to the gate oxidecapacitance, as in the accumulation case. At higher frequencies, C_(T)will coincide with that at low frequencies for V_(g)<V_(t); however, forV_(g)>V_(t), the electron (inversion layer) concentration will not beable to follow the ac signal and the depletion region capacitance willlead to smaller C_(T), producing a smaller time constant than in theaccumulation regime. For example, we calculated C_(T)=9.47×10⁻¹⁷ F/μmfor V_(g)=20 V and ac frequency of 1 MHz. This suggests that even higherspeed-operation can be achieved with the depletion mode than with theaccumulation mode. Note that, in this case, since the depletion regionwidth remains constant for V_(g)>V_(t) (constant capacitance), theoptical losses of the structure will be approximately constant forV_(g)>V_(t), and equal to the minimum value obtained in the dc analysis(7.67 dB/cm for the first embodiment, and 18.95 dB/cm for the second,metal contact embodiment).

The threshold voltage of the inversion configuration (FIG. 5A) wasestimated to be −1.42 V. This means that the MOS diode will work mainlyunder strong inversion conditions. Therefore, due to the aforementionedinability of minority carriers to follow high frequency electricalsignals, we can infer that the inversion-mode configuration is notappropriate for high-speed electro-optic modulation.

Thus, for small signal ac operation either the accumulation- or thedepletion modes could be considered. The former exhibits less loss,while the latter may operate at higher frequency.

A large-signal transient (pulse operation) study of the accumulation-and depletion-mode structures may be carried out by using ATLAS. A100-ns-long gate voltage pulse with OFF-state gate voltage V_(g,OFF)=0Vand ON-state gate voltage V_(g,ON)<0 for accumulation and V_(g,ON)>0 fordepletion, may be applied to the simulated device. Rise and fall timesof the voltage pulse were equal to 10 ps. FIG. 12A shows the calculatedΔn_(eff) for the accumulation- and depletion-mode configurations underpulse operation as a function of |V_(g,ON)|. The dc operation curve forthe depletion mode has been also included for comparison purposes. Thevariation of Δn_(eff) corresponding to the accumulation is the same forboth dc and transient operations. However, a significant Δn_(eff)increase is observed for the depletion case when it is pulse-operated ascompared to the dc operation for gate voltages equal or higher than thethreshold voltage (V_(t)=14.9 V). This is because, for those gatevoltages, the device is operated under deep depletion conditions: theinversion layer is not or is only partially formed since the generationof minority carriers cannot keep up with the amount needed to form theinversion layer and, therefore, the depletion layer can increase beyondits maximum steady-state value, resulting in a capacitance that furtherdecreases with voltage. The rate of change of the gate voltage (pulseramp slope) required to observe deep depletion is given by:

$\begin{matrix}{\frac{V_{g}}{t} > {\frac{{qn}_{i}}{2C_{gox}}\sqrt{\frac{\mu_{n}V_{t}}{\tau_{n}}}}} & \lbrack 3\rbrack\end{matrix}$

where q is the electron charge, n_(i) (≈10¹⁰ cm⁻³ at 300 K) is theintrinsic carrier concentration of Si, C_(gox) (=2.22×10⁻⁸ F/cm²) is theoxide capacitance per unit area, and μ_(n) (=1000 cm²/Vs at 300 K) isthe electron mobility. Thus, (dV_(g)/dt) should be higher than 5.2×10³V/s, which is easily accomplished by ramp times employed in high-speeddigital signals.

The absence of the inversion layer in the depletion-mode device underpulse operation also leads to a decrease of the transmission lossesunder deep depletion operation as shown in FIG. 12B for the firstembodiment and FIG. 12C for the second, metal contact embodiment.

For depletion, gate voltages higher than 20 V may lead to an electricfield in the semiconductor beneath the gate oxide higher than 3×10⁵V/cm, which is the breakdown electric field in Si. This imposes alimitation on the allowed gate voltage (20 V) and, therefore, on themaximum effective refractive index change (2.5×10⁴) and minimumtransmission losses (6.37 dB/cm for the first embodiment, or 17.82 dB/cmfor the second embodiment) that can be obtained under deep depletionoperation.

Table II shows the calculated turn-on and turn-off times of theaccumulation and depletion devices for different ON-state gate voltages.The turn-on (turn-off) time is defined as the time needed for thecarrier concentration to reach its maximum (minimum) value when the gatevoltage is stepped from V_(g,OFF) (V_(g,ON)) to V_(g,ON) (V_(g,OFF)).Switching times (turn-on time+turn off time) on the order of tens of psare predicted, the depletion operation being slightly faster than theaccumulation, as expected from the small-signal analysis.

TABLE II Accumulation Depletion |V_(g,ON)| (V) Turn-on (ps) Turn-off(ps) Turn-on (ps) Turn-off (ps) 5 25.5 25.5 10.5 12.7 10 25.5 25.5 12.512.7 15 19.1 36.3 14.7 12.2 20 19.1 34.9 14.3 11.9 25 19.1 33.1 15.111.6 30 19.1 32.5 16.8 11.3

Electro-Optic Microresonator Modulator

The transmission of an optical resonator is highly sensitive to smallindex changes, making it ideal for intensity modulation in a shortlength. Thus, a suitable application of the studied configuration is awaveguide intensity modulator based on a microring resonator as thatshown in FIG. 13. R is the radius of a ring waveguide 1310 formed on ap-silicon layer 1312 with gate 1313 formed on top, and d_(g) is thespacing between the ring and bus waveguides 1315 and 1320 (d_(g) is thesame for both buses). A MOS diode with p+ regions 1322 and 1323, andwith h_(gox)=200 nm is used to change the refractive index in the ringwaveguide. The resulting phase change in the ring is converted into anintensity variation at the output port at the operation (probe)wavelength.

The output transmissivity (out port) of the microring modulator may beestimated by using the transfer matrix method. Bending losses werecalculated by employing the BPM, and the spacing between ring and buswaveguides was estimated by using the finite difference time domainmethod (FDTD). The ring radius and the power-coupling coefficient(|κ²|), which is related to d_(g), will determine the main resonatorparameters: quality factor Q (=ω₀/Δω_(FWHM), with ω₀ the resonancefrequency and Δω_(FWHM) the full frequency width at half maximum),cavity lifetime τ_(ph) (=Q/ω₀), and total internal loss A_(i)[=(α_(T)+α_(bend))2πR, with α_(T) the transmission losses and α_(bend)the bending losses]. For optimum performance, it is required: high Q,for high modulation; small τ_(ph), for high switching speed; and lowA_(i), for high transmittance. In order to have a resonance at the probewavelength λ_(probe)=1550 nm, the ring radius must also satisfy thecondition 2πR=m (λ_(probe)/2n_(eff)), where m is an integer andn_(eff)=n_(eff,OFF)+Δn_(eff), with n_(eff,OFF) being the effective indexin the OFF state (V_(g)=0V) and Δn_(eff) being the variation of theeffective refractive index when a gate voltage is applied (ON state).For the unbiased case, a trade-off among the aforementioned ringparameters is found for R=6.9 μm and |κ|²=0.012, which corresponds to agap spacing d_(g)=490 nm. This results, for the accumulation case, inQ=2.82×10⁴, τ_(ph)=23.2 ps and A_(i)=0.028 dB (α_(T)=3.6 dB/cm andα_(bend)=2.9 dB/cm). For the depletion case, we obtain Q=2.14×10⁴,τ_(ph)=17.6 ps and A_(i)=0.065 dB (α_(T)=8.6 dB/cm and α_(bend)=6.4dB/cm). Note that the bending losses are higher for depletion becausethe refractive index of the core waveguide at zero bias is smaller (dueto the background doping of 2×10¹⁷ cm⁻³) than that of the accumulationcase; thus, the index contrast between the Si core and the oxidecladding is reduced, resulting in a weaker optical confinement in thebent waveguide (higher radiation losses) than that obtained for theaccumulation case. It is also seen, that for the same ring parameters,the depletion device exhibits a poorer Q than the accumulation devicedue to the higher losses (both transmission and bend) in the former.

The value of τ_(ph) for the depletion device is higher than the turn-onand turn-off times due to carrier distribution (Table II), meaning thatthe switching speed for this configuration will be limited byτ_(ph)=17.6 ps. For the accumulation device, the calculated turn-on andturn-off times due to carrier dynamics (Table II) at low voltageoperation (5 V and 10 V) are higher than the photon lifetime of the ring(23.3 ps); therefore, the carrier-induced transient times will limit theswitching speed of the ring modulator for the accumulationconfiguration.

The modulation depth (M) of the microring modulator at a givenwavelength is defined as (P_(OFF)−P_(ON))P_(OFF), where P_(OFF) andP_(ON) are the transmitted output power (out port) in the OFF and ONstates, respectively. FIG. 14 shows the transmission characteristics(output port) for the aforementioned ring parameters (R=6.9 μm and|κ²|=0.012) for the accumulation mode configuration. The refractiveindex in the cavity is modulated between V_(g)=0V (Δn=0, OFF state) andV_(g)=−5V (Δn=−6.3×10⁻⁵, ON state). The obtained modulation depth andtransmittivity at the probe wavelength, 1550.014 nm, are 73.4% and 59%,respectively. We calculated the modulation depth for the accumulationand depletion operation modes as a function of the gate voltage (FIG.15). Pulse operation (section IV.C) is assumed for both modes. The probewavelengths, 1550.014 nm for accumulation and 1549.975 nm for depletion,have been chosen in order to obtain a transmittivity (T) value of 59%and 23% for the accumulation and depletion modes, respectively, in theOFF-state. It is seen that modulation depths higher than 73% can beachieved under the accumulation operation mode for |V_(g)|≧5 V. Notethat, despite higher values of |Δn_(eff)| are obtained under depletionthan under accumulation for |V_(g)|≧10 V (see FIG. 6 a), the modulationdepth is higher for the latter. This is due to the aforementioned higherlosses exhibited by the depletion configuration, which degrades thequality factor of the resonator, and therefore, the achievablemodulation depth.

Due to the non-negligible value of the thereto-optic effect in Si(dn/dT≈2×10⁻⁴ K⁻¹), temperature effects on the index should be minimizedin the studied configurations. This can be achieved by employing strainsilicon waveguide introduced in the fabrication process by, for example,controlling the overcladding deposition conditions. The introducedstrain induces a decrease of the refractive index with temperature,which counterbalances the thermo-optic effect in silicon.

In a further embodiment, the transmission at the resonance wavelength ofan optical cavity is highly sensitive to small index changes, makingthem ideal for intensity modulation in a short length. Thus, animmediate application of the studied configuration is a straightwaveguide intensity modulator based on a microcavity illustratedgenerally at 1600 in FIG. 16. FIG. 16 is a schematic of ahigh-index-contrast rib SOI waveguide 1610 microcavity in which air (orSiO₂-filled) holes 1615 have been defined in order to provide ahigh-index-contrast periodic structure [one-dimensional photoniccrystal]. A MOS diode indicated generally at 1605 with h_(gox)=200 nm isused to change the refractive index in the cavity region. Diode 1615 hasa gate 1620 formed over a center portion of waveguide 1610, between setsof holes 1615. Ground contacts 1625 are formed adjacent the waveguide1610. The waveguide 1610 and diode 1605 are formed on an oxide 1630supported by a silicon substrate 1635 in one embodiment. Other materialsmay be used in further embodiments.

The performance of the device assuming that the microcavity is estimatedequivalent to a Fabry-Perot (F-P) cavity defined by distributed Braggreflectors of reflectivity R, diffraction losses D, cavity length a_(d)and internal losses A_(c). The transmission characteristics of theresonator may be calculated by using the equation:

$\begin{matrix}\begin{matrix}{{T(\lambda)} = {{T_{lm}(\lambda)}\left\lbrack {1 - D} \right\rbrack}} \\{= {\left( \frac{{A_{c}\left( {1 - R} \right)}^{2}}{\left( {1 - {A_{c}R}} \right)^{2} + {4A_{c}R\; {\sin^{2}\left( \frac{2\pi \; n_{eff}a_{d}}{\lambda} \right)}}} \right) \cdot \left\lbrack {1 - D} \right\rbrack}}\end{matrix} & \lbrack 4\rbrack\end{matrix}$

where T_(lm)(λ) is the transmittivity of the lossless-mirrors F-Pcavity. n_(eff)=n_(eff,OFF)+Δn_(eff), where n_(eff,OFF) (=2.52 is theeffective index in the OFF state (V_(g)=0V) and Δn_(eff) is thevariation of the effective refractive index when a gate voltage isapplied (ON state). The following values were assumed: R=97% [8], D=17%[8], a_(d)=21.56 μm [≈70(1.55 μm/2n_(eff,OFF)]. The considered values ofA_(c) are those shown in FIG. 12A. The modulation depth (M) at a givenwavelength is defined as (P_(OFF)−P_(ON))/P_(OFF), where P_(OFF) andP_(ON) are the transmitted power in the OFF and ON states, respectively.

FIG. 17 shows the calculated modulation depth for the accumulation anddepletion operation modes as a function of the gate voltage. Pulseoperation is assumed for both modes. The probe wavelengths, 1550.04 nmfor accumulation and 1549.91 nm for depletion, have been chosen in orderto obtain a transmittivity (T) value of 50% and 33% for the accumulationand depletion modes, respectively, in the OFF-state (zero bias). It isseen than modulation depths higher than 19% can be achieved under theaccumulation operation mode for |V_(g)|≧5 V. As expected from FIG. 12A,for |V_(g)|≦7 V, the accumulation mode provides higher modulation,whereas for |V_(g)|≧7 V, the depletion device exhibits highermodulation. The modulation could be increased by increasing the cavitylength; however, this would lead to a significant reduction oftransmission due to the cavity losses (gate electrode losses).Therefore, a trade-off between modulation and transmission must beconsidered.

FIG. 18 shows the transmission characteristics of a 21.56-μm-long cavityfor the accumulation mode configuration. The refractive index in thecavity is modulated between V_(g)=0V (OFF state) and V_(g)=−5V(Δn=−6×10⁻⁵, ON state). The modulation depth and transmittivity at theprobe wavelength, 1550.04 nm, are 19.3% and 50%, respectively. Note thatthe probe wavelength is not chosen at exactly the resonance peak, 1.55μm, but slightly shifted towards one of the lobe slopes (λ_(p)=1.55004μm) in order to obtain maximum modulation depth.

The photon lifetime (τ_(ph)) of the 21.56-μm-long resonator, that is,the time for the stored energy in the cavity to vanish after theexternal supply is shut off, was estimated to be 4.8 ps[=λ_(r)/Δλ_(1/2), where λ_(r) is the resonance wavelength (=1.55 μm) andΔλ_(1/2) is the full width at half maximum at the resonance wavelength].The value of τ_(ph) is smaller than the switching times obtained insection IV.C, meaning that the transient response of the modulator willbe determined by the hole concentration dynamic distribution (switchingtimes on the order of 10 ps).

The order of magnitude of |Δn_(eff)| achievable in the studiedconfigurations is on the same order of magnitude than that produced bythe thermo-optic effect in Si (dn/dT≈2×10⁻⁴ K⁻¹). This implies that inorder to avoid undesired thermo-optic effects an accurate control of thedevice (or chip) temperature is necessary. In addition, an accuratecontrol of the probe wavelength and/or of the cavity length is desiredfor optimum operation of the modulator.

For the sake of comparison, Table III shows a list of proposedall-silicon electro-optic modulators recently reported in theliterature. The MOS device analyzed in this work is expected to improvesignificantly previous designs in terms of switching time and dc powerconsumption

TABLE III DC Electrical Optical M Power t_(s) Length structure structure(%) (mW) (ns) (μm) Prior devices p-i-n Bragg 50 4 24.7 3200 reflectorPrior devices BMFET FCAM 20 126 6 1000 Prior devices p-i-n Mach- >90 21060 1110 Zehnder Prior devices BMFET Y-junction 92 ~350 16 5000 Priordevices p-i-n Bragg 94 0.3 5 3200 reflector Prior devices p-i-nMach- >90 ~0.56 0.51 >500 Zehnder Prior devices p-i-n F-P 80 0.014 1.310 Prior devices MOS Mach- 97.5 ~0.0 ~0.6 10000 Zehnder Our device MOSF-P 19 ~0.0 0.023 22

Electro-optic MOS SOI high-index-contrast waveguide modulators have beendescribed for 1.55-μm operation wavelength. The real refractive indexand absorption coefficient of the core Si waveguide are changed by usingthe free-carrier dispersion effect produced by a MOS diode. A gate oxidethickness of 200 nm has been shown to be a good tradeoff between lowgate electrode losses and low bias voltage operation. Both accumulationand depletion operation modes are well suited for high-speedapplications, with the former mode exhibiting lower loss. Modulationdepths of 73% for a first embodiment, and greater than or equal toapproximately 19% for the second metal gate embodiment, and switchingtimes on the order of tens of picoseconds are predicted for biasvoltages of only 5 V or higher. The studied electro-optic modulator istherefore a very promising candidate for implementing Si micro- andnano-photonic integrated circuits for high-speed applications.

MOS and Geometries for Integrating MOS and Pin.

MOS can lead to very high speed (perhaps tend to hundreds of G Gbpsec.However, the pin can also work for high speed, perhaps not as high asthe MOS but very high (at least 10 Gbpsec). Electro-optic devices suchas that shown in FIG. 5B, may be based on MOS structures. The use of aMOS diode should lead to high speed operation than the p-i-n structure(limited by carrier diffusion) since the carrier distribution in thesemiconductor is governed by a drift mechanism (electric field). In aMOS structure however, significant large concentration variations arepossible only within small areas beneath the insulated gate region 531.This produces a small overlap between the optical mode and thenon-equilibrium charge distribution in the waveguide, leading to asmaller effective index variation in a MOS system than that in a p-i-nconfiguration. A small index change requires a very long structure, onthe order of millimeter, in order to induce a significant modulationdepth. A micron-size MOS-based high-index-contrast SOI waveguide forhigh-speed electro-optic modulation in Si is based on strong lightconfinement. The light confinement enhances the effect of small indexchanges on the transmission of the device enabling, an ultra-compactstructure with high modulation depth. FIG. 5A shows a schematiccross-section of a MOS-waveguide configuration. The structure consist ofa high aspect ratio [rib height (200 nm)>>slab height (50 nm)] rib SOIwaveguide 511 with highly doped regions (10¹⁹ cm⁻³) defined in the slab541 at each side of the rib. The rib cross section height and widthdimension are typical of a 1.55-μm-wavelength high-index-contrast stripSOI waveguide in order to guarantee single mode operation. The speed ofthe device is limited by its capacitance. Using a gate oxide 531 of 200nm, the time constant τ_(c)=RC_(T) of the device results to be 5×10⁻¹⁵s/μm. For example, for a 20-μm-long device, τ_(c)=1×10⁻¹ ps, indicatingthe suitability of this configuration for high-speed operation. A changein index of approximately 6×10⁻⁵ under 5V and transmission losses of 15dB/cm in the MOS region is estimated.

Novel light confinement geometries for modulators and switches in theform of 2D guided-wave structures, such as four port devices for routingsignals on-chip (see FIGS. 19 and 20). Note that cavities with extremelyhigh Q, such as for example photonic crystal cavities, may have highlosses and bandwidth limitations. Both p-i-n and MOS configurations areconsidered. The spectral properties, WDM capabilities, bandwidth,modulation depth, size and power dissipation of the devices areinvestigated with the aim of optimizing the driver performance.

Both devices are based on ring resonators. The resonant nature of thedevice induces high sensitivity to small index changes making them idealfor high modulation depth at low drive powers for very compact devices.

An example p-i-n structure to be investigated is illustrated at 1900 inFIG. 19. A complex refractive index of the ring 1910 is changed byapplying voltage 1915 across anode and cathode probe pads leading tostrong modulation. Preliminary calculations show that modulation depthlarger than 90% can be achieved close to the resonant wavelength, withdc power consumption of only 1.53 μW/μm for a ring with Q=λ/Δλ=3000.This low dissipated power leads to a negligible increase of the devicetemperature, less than 10⁻² K. From calculations similar to the onespreviously shown, it may be estimated that the on-off switching timesfor such a device may be as small as 50 psec and modulation speedslarger than 5 GHz may be obtained. For smaller modulation depths (˜20%),speeds in the tens of GHz range may be obtained.

An example of an MOS structure is shown at 2000 in FIG. 20. The use of aMOS diode leads to high speed operation since the carrier distributionin the semiconductor is governed by a drift mechanism (electric field).A gate electrode 2010 is placed close to the top of the ring resonator2015. The silicon layer (device layer) has a background dopingconcentration of 10¹⁵ cm⁻³. The device can be operated in accumulationand depletion mode depending on the gate bias. The exact geometry of thedevice may be defined so that the losses, due to the overlap of the modewith the highly-doped regions and gate, will be minimized. Preliminarycalculations show that a maximum modulation depth of 20% for a ringresonator of Q=3000, using a gate oxide of 100 nm can be achieved usinga bias voltage of 5 V.

In order to achieve higher modulation depths, rings with higher Q's maybe used. This may be achieved using: 1. a larger distance between theincoming waveguide and the ring resonator than 100 nm, 2. minimizinglight scattering in the waveguides due to sidewall roughness by specialfabrication methods such as oxidations and 3. using a thicker gateoxide, in order to minimize absorption in the ring.

Electro-optic modulators in the form of ring or disc waveguideresonators and other types of resonators, such as photonic crystalcavities and other cavities that may operate as resonators, may bevaried in size. Diameters of ring or disc resonators may be betweenapproximately 10 to 14 um. Other size modulators may also be utilized,such as 30 um diameter modulators and larger or smaller. In oneembodiment, the diameter is less than 500 um in diameter.

The Abstract is provided to comply with 37 C.F.R. §1.72(b) to allow thereader to quickly ascertain the nature and gist of the technicaldisclosure. The Abstract is submitted with the understanding that itwill not be used to interpret or limit the scope or meaning of theclaims.

1. A method comprising: providing light to a waveguide optically coupledto an optical resonator; modulating the light in the waveguide byvarying the optical coupling of the optical resonator to the waveguide.2. The method of the claim 1 wherein the optical coupling is varied bychanging a free carrier concentration in the optical resonator to varythe refractive index of the optical resonator.
 3. The method of claim 1wherein the optical resonator is a ring resonator.
 4. The method ofclaim 1 wherein the optical resonator is a Fabry-Perot resonator.
 5. Themethod of claim 1 wherein the optical resonator is an optical cavity. 6.The method of claim 1 and further comprising providing a p doped regionand an n doped region adjacent to the optical resonator.
 7. The methodof claim 6 wherein the doped regions are heavily doped.
 8. The method ofclaim 7 wherein the heavily doped regions form a p-i-n diode about theoptical resonator.
 9. The method of claim 1 wherein the free carrierconcentration is changed by at least one of injection, accumulation,depletion and inversion of carriers.
 10. The method of claim 2 whereinthe carrier concentration is changed by a p-i-n diode.
 11. The method ofclaim 2 wherein the carrier concentration is changed bymetal-oxide-semiconductor field-effect-transistor.
 12. A methodcomprising: providing light to a optical ring resonator; modulating thelight in the optical ring resonator by changing its refractive index.13. The method of claim 12 wherein the refractive index is changed byvarying a free carrier concentration in the optical ring resonator. 14.The method of claim 12 where the light is provided to the optical ringresonator by an optically coupled waveguide.
 15. The method of claim 12and further comprising providing a p doped region and an n doped regionadjacent to the optical ring resonator.
 16. The method of claim 15wherein the doped regions are heavily doped.
 17. The method of claim 16wherein the heavily doped regions form a p-i-n diode about the opticalring resonator.
 18. The method of claim 12 wherein the free carrierconcentration is changed by at least one of injection, accumulation,depletion and inversion of carriers.
 19. The method of claim 18 whereinthe carrier concentration is changed by metal-oxide-semiconductorfield-effect-transistor about the optical ring resonator.
 20. A methodcomprising: providing light to a waveguide; modulating the light in thewaveguide by changing the refractive index of an optical resonatorcoupled to the waveguide.
 21. The method of claim 20 wherein therefractive index is changed by changing the free carrier concentrationin the optical resonator.
 22. The method of claim 21 wherein varying therefractive index changes optical coupling of the optical waveguide tothe waveguide.